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What is the 25th term of the arithmetic progression (AP) defined by the sequence -5, -5/2, 0, 5/2,...?

(A) 15
(B) 13
(C) 12.5
(D) 14

User Medhdj
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1 Answer

4 votes

Final answer:

The 25th term of the arithmetic progression is found using the formula Tn = a + (n - 1)d. With a first term of -5 and a common difference of 5, the 25th term is 115, which does not match any of the provided options.

Step-by-step explanation:

The question is asking to find the 25th term of the arithmetic progression (AP) with the first few terms being -5, -5/2, 0, 5/2,.... To find any term in an arithmetic progression, we can use the formula:

Tn = a + (n - 1)d

where Tn is the n-th term, a is the first term, d is the common difference, and n is the term number.

In this sequence, the first term a = -5 and the difference between the terms d = 5/2 - (-5) which is 5/2 + 5/2 or 5. Now we can use these values to find the 25th term with the formula:

T25 = -5 + (25 - 1) × 5

Calculating the above expression, we get:

T25 = -5 + (24 × 5)

T25 = -5 + 120

T25 = 115

Thus, the 25th term of the given arithmetic progression is 115, which is not listed in the provided options.

User Johnathan
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